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A new edition of this popular text on robust statistics, thoroughly updated to include new and improved methods and focus on implementation of methodology using the increasingly popular open-source software R. Classical statistics fail to cope well with outliers associated with deviations from standard distributions. Robust statistical methods take into account these deviations when estimating the parameters of parametric models, thus increasing the reliability of fitted models and associated inference. This new, second edition of Robust Statistics: Theory and Methods (with R) presents a broad coverage of the theory of robust statistics that is integrated with computing methods and applications. Updated to include important new research results of the last decade and focus on the use of the popular software package R, it features in-depth coverage of the key methodology, including regression, multivariate analysis, and time series modeling. The book is illustrated throughout by a range of examples and applications that are supported by a companion website featuring data sets and R code that allow the reader to reproduce the examples given in the book. Unlike other books on the market, Robust Statistics: Theory and Methods (with R) offers the most comprehensive, definitive, and up-to-date treatment of the subject. It features chapters on estimating location and scale; measuring robustness; linear regression with fixed and with random predictors; multivariate analysis; generalized linear models; time series; numerical algorithms; and asymptotic theory of M-estimates. Explains both the use and theoretical justification of robust methods Guides readers in selecting and using the most appropriate robust methods for their problems Features computational algorithms for the core methods Robust statistics research results of the last decade included in this 2nd edition include: fast deterministic robust regression, finite-sample robustness, robust regularized regression, robust location and scatter estimation with missing data, robust estimation with independent outliers in variables, and robust mixed linear models. Robust Statistics aims to stimulate the use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. It is an ideal resource for researchers, practitioners, and graduate students in statistics, engineering, computer science, and physical and social sciences.
This book presents recent developments in multivariate and robust statistical methods. Featuring contributions by leading experts in the field it covers various topics, including multivariate and high-dimensional methods, time series, graphical models, robust estimation, supervised learning and normal extremes. It will appeal to statistics and data science researchers, PhD students and practitioners who are interested in modern multivariate and robust statistics. The book is dedicated to David E. Tyler on the occasion of his pending retirement and also includes a review contribution on the popular Tyler’s shape matrix.
The majority of data sets collected by researchers in all disciplines are multivariate, meaning that several measurements, observations, or recordings are taken on each of the units in the data set. These units might be human subjects, archaeological artifacts, countries, or a vast variety of other things. In a few cases, it may be sensible to isolate each variable and study it separately, but in most instances all the variables need to be examined simultaneously in order to fully grasp the structure and key features of the data. For this purpose, one or another method of multivariate analysis might be helpful, and it is with such methods that this book is largely concerned. Multivariate analysis includes methods both for describing and exploring such data and for making formal inferences about them. The aim of all the techniques is, in general sense, to display or extract the signal in the data in the presence of noise and to find out what the data show us in the midst of their apparent chaos. An Introduction to Applied Multivariate Analysis with R explores the correct application of these methods so as to extract as much information as possible from the data at hand, particularly as some type of graphical representation, via the R software. Throughout the book, the authors give many examples of R code used to apply the multivariate techniques to multivariate data.
Classical statistical techniques fail to cope well with deviations from a standard distribution. Robust statistical methods take into account these deviations while estimating the parameters of parametric models, thus increasing the accuracy of the inference. Research into robust methods is flourishing, with new methods being developed and different applications considered. Robust Statistics sets out to explain the use of robust methods and their theoretical justification. It provides an up-to-date overview of the theory and practical application of the robust statistical methods in regression, multivariate analysis, generalized linear models and time series. This unique book: Enables the reader to select and use the most appropriate robust method for their particular statistical model. Features computational algorithms for the core methods. Covers regression methods for data mining applications. Includes examples with real data and applications using the S-Plus robust statistics library. Describes the theoretical and operational aspects of robust methods separately, so the reader can choose to focus on one or the other. Supported by a supplementary website featuring time-limited S-Plus download, along with datasets and S-Plus code to allow the reader to reproduce the examples given in the book. Robust Statistics aims to stimulate the use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. It is ideal for researchers, practitioners and graduate students of statistics, electrical, chemical and biochemical engineering, and computer vision. There is also much to benefit researchers from other sciences, such as biotechnology, who need to use robust statistical methods in their work.
This text presents methods that are robust to the assumption of a multivariate normal distribution or methods that are robust to certain types of outliers. Instead of using exact theory based on the multivariate normal distribution, the simpler and more applicable large sample theory is given. The text develops among the first practical robust regression and robust multivariate location and dispersion estimators backed by theory. The robust techniques are illustrated for methods such as principal component analysis, canonical correlation analysis, and factor analysis. A simple way to bootstrap confidence regions is also provided. Much of the research on robust multivariate analysis in this book is being published for the first time. The text is suitable for a first course in Multivariate Statistical Analysis or a first course in Robust Statistics. This graduate text is also useful for people who are familiar with the traditional multivariate topics, but want to know more about handling data sets with outliers. Many R programs and R data sets are available on the author’s website.
Information theory and inference, taught together in this exciting textbook, lie at the heart of many important areas of modern technology - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics and cryptography. The book introduces theory in tandem with applications. Information theory is taught alongside practical communication systems such as arithmetic coding for data compression and sparse-graph codes for error-correction. Inference techniques, including message-passing algorithms, Monte Carlo methods and variational approximations, are developed alongside applications to clustering, convolutional codes, independent component analysis, and neural networks. Uniquely, the book covers state-of-the-art error-correcting codes, including low-density-parity-check codes, turbo codes, and digital fountain codes - the twenty-first-century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, the book is ideal for self-learning, and for undergraduate or graduate courses. It also provides an unparalleled entry point for professionals in areas as diverse as computational biology, financial engineering and machine learning.
Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.
Multivariate statistics refer to an assortment of statistical methods that have been developed to handle situations in which multiple variables or measures are involved. Any analysis of more than two variables or measures can loosely be considered a multivariate statistical analysis. An introductory text for students learning multivariate statistical methods for the first time, this book keeps mathematical details to a minimum while conveying the basic principles. One of the principal strategies used throughout the book--in addition to the presentation of actual data analyses--is pointing out the analogy between a common univariate statistical technique and the corresponding multivariate method. Many computer examples--drawing on SAS software --are used as demonstrations. Throughout the book, the computer is used as an adjunct to the presentation of a multivariate statistical method in an empirically oriented approach. Basically, the model adopted in this book is to first present the theory of a multivariate statistical method along with the basic mathematical computations necessary for the analysis of data. Subsequently, a real world problem is discussed and an example data set is provided for analysis. Throughout the presentation and discussion of a method, many references are made to the computer, output are explained, and exercises and examples with real data are included.
This book is open access under a CC BY 4.0 license This open access book brings together the latest genome base prediction models currently being used by statisticians, breeders and data scientists. It provides an accessible way to understand the theory behind each statistical learning tool, the required pre-processing, the basics of model building, how to train statistical learning methods, the basic R scripts needed to implement each statistical learning tool, and the output of each tool. To do so, for each tool the book provides background theory, some elements of the R statistical software for its implementation, the conceptual underpinnings, and at least two illustrative examples with data from real-world genomic selection experiments. Lastly, worked-out examples help readers check their own comprehension.The book will greatly appeal to readers in plant (and animal) breeding, geneticists and statisticians, as it provides in a very accessible way the necessary theory, the appropriate R code, and illustrative examples for a complete understanding of each statistical learning tool. In addition, it weighs the advantages and disadvantages of each tool.